The present invention relates to a new and distinct cultivar of Begonia, of the family Begoniaceae, and given the cultivar name, ‘TNBEGRM’. This plant originated from a test cross with an unnamed Begonia boliviensis hybrid as the pollen parent. The new cultivar originated from a cross between Begonia hemsleyana unnamed hybrid (unpatented), as the seed parent and Begonia boliviensis hybrid unnamed (unpatented), as the pollen parent. There are no similar Begonia on the market known to the inventor. This selection is uniquely characterized by:                1. leaves colored burgundy to silvered burgundy with olive green along veins,        2. dark burgundy red leaf backs,        3. medium pink flowers,        4. a trailing habit, and        5. excellent vigor.        
Compared to the seed parent Begonia hemsleyana hybrid unnamed, an unpatented plant, the new cultivar has leaves a trailing rather than an upright, shrubby habit and dark simple leaves rather than green to silver palmately compound.
Compared to the pollen parent, Begonia boliviensis hybrid unnamed, an unpatented plant, the new cultivar is trailing rather than sprawling, with smaller flowers that are pink rather than red orange, and maroon leaves instead of green.
The new variety has been reproduced only by asexual propagation (leaf cuttings and tissue culture). Each of the progeny exhibits identical characteristics to the original plant. Asexual propagation by micropropagation using the meristem as done in Canby, Oreg., shows that the foregoing characteristics and distinctions come true to form and are established and transmitted through succeeding propagations. The present invention has not been evaluated under all possible environmental conditions. The phenotype may vary with variations in environment without a change in the genotype of the plant.